The maximum distance between the inter-atomic planes of a crystal is $10^{-7} \ cm$. The maximum wavelength of $X$-rays that can be studied by this crystal is ........... $\mathring{A}$.

For the production of $X$-rays, the target should be made of

The $K_{\alpha}$ $X$-ray of molybdenum has a wavelength of $0.071 \, nm$. If the energy of a molybdenum atom with a $K$ electron knocked out is $27.5 \, keV$,the energy of this atom when an $L$ electron is knocked out will be $.... \, keV$. (Round off to the nearest integer) $[h = 4.14 \times 10^{-15} \, eVs, c = 3 \times 10^{8} \, ms^{-1}]$

The minimum wavelength of $X$-rays emitted by an $X$-ray tube is $0.4125 \mathring{A}$. The accelerating voltage is ...... $kV$.

An $X$-ray tube operates at $50 \, kV$ and $20 \, mA$. The target material has a mass of $1.0 \, kg$ and a specific heat capacity of $495 \, J \cdot kg^{-1} \cdot ^\circ C^{-1}$. One percent of the applied electrical power is converted into $X$-rays,and the remaining energy is used to heat the target. Then:
$(1)$ $A$ suitable target material should have a high melting point.
$(2)$ $A$ suitable target material should have low thermal conductivity.
$(3)$ The rate of rise of temperature of the target is $2 \, ^\circ C/s$.
$(4)$ The minimum wavelength of the emitted $X$-rays is $0.25 \, \mathring{A}$.

In radiotherapy,$X$-rays are used to